Parametric analysis of wind action on slab

8/20/2019 Parametric analysis of wind action on slab

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Eng. Rev. 31-1 (2011) 45-54 45 _______________________________________________________________________________________________________________________

UDC 624.073:624.26.042.41:551.556:006.35

PARAMETRIC ANALYSIS OF WIND ACTION ON SLAB BRIDGE

DECK

Ivana ŠTIMAC GRANDIĆ – Ana IVANČIĆ – Bojan LIKER

Abstract: In this paper, the parametric analysis of wind action on the bridge deck is conducted. Wind forceacting on the bridge deck is calculated varying upon the following parameters: wind area, terrain category,road restraint system and height of the deck above ground. The presented results show the possibility of great changes in wind force due to changes of the listed parameters. Since a similar slab bridge deck is oftenused in different locations in Croatia, it is important to bear in mind when designing standardised bridgesthe fact that the wind load on bridges in different locations can change several times.

Keywords: – wind action –

parametric analysis – EN 1991-1-4

1. INTRODUCTION

Wind action, besides earthquake, makes up thedominant horizontal effect on structures in theirlifetime. In particular, the significance of theseactions, which are variable in time and in intensity,varies depending on the meteorological andseismological characteristics of a certain area.In the design of dynamically sensitive structures

(e.g. suspension bridges [1]), whose behaviordepends on the dynamic motion of the structure andthe dynamic character of the load, it is necessary tocarry out the calculation of the dynamic response ofstructures by using the dynamic response procedure,such as modal analysis. Wind load on the dynamicinsensitive structure can be treated as quasi-static, soa dynamic response procedure is not needed.Technical regulations, aimed at ensuring conditionsfor joining the common European market, takinginto account the principles of the Europeanharmonization of technical legislation [2-6], refer toa series of European standards for design(Eurocodes) which ensure the fulfillment of theessential requirements for building according toConstruction Product Directive [7]. These Europeanstandards are adopted as the Croatian standard (HREN). Wind load on structures is defined by standardEN 1991-1-4 [8] and associated National Annex.In the past decade, several papers dealing with the problem of determining the nationally defined

parameters for the modelling of wind load in Croatiawere published [9-12]. Due to the fact that the National Annexes are still under revision, in this paper the National Annex for the draft standardENV [13] will be used because huge changes in the National Annex for standard EN 1991-1-4 are notexpected.

2. WIND ACTIONS ACCORDING TO EN

1991-1-4

2.1. General

EN 1991-1-4 gives guidance on the determination ofnatural wind actions for the structural design of building and civil engineering works for each of theloaded areas under consideration. This includes thewhole structure or parts of the structure or elementsattached to the structure. This standard is applicableto bridges with a span of up to 200 m, with theexception of cable supported bridges.

The wind action is represented by a simplified set of pressures or forces whose effects are equivalent tothe extreme effects of the turbulent wind. In general,wind pressure on the structure or structural elementacts perpendicular to the surface, except whereotherwise provided, for example, in the tangentialfriction force on the bridge deck surface. The windactions calculated using EN 1991-1-4 [8] are


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46 I. Š. Grandić , A. Ivanč ić , B. Liker:Parametric Analysis of Wind… _______________________________________________________________________________________________________________________

characteristic values determined from the basicvalues of wind velocity or the velocity pressure.

2.2. Wind action on bridges

According to the standard EN 1991-1-4 [8], adynamic response procedure is generally not neededfor normal road and railway bridge decks of lessthan a 40 m span, bridges of a constant depthconsisting of a single deck with one or more spans.For the purpose of this categorization, normal bridges are bridges constructed in steel, concrete,aluminum or timber, including compositeconstruction, and whose shape of cross sections isgenerally covered by Figure 1.Wind actions on bridges produce forces in the threedirections as shown in Figure 2 where the x– direction is the direction parallel to the deck width,

perpendicular to the span, the y–direction is thedirection along the span and the z–direction is thedirection perpendicular to the deck. L is length inthe y–direction, b is the width in the x–direction andd is the depth in the z–direction.The dominant component of the wind action on the bridge is the force in the x–direction [14], thereforeonly that component will be analyzed in this paper.

2.2.1. Wind force in x-direction

Where it has been assessed that a dynamic response procedure is not necessary, the wind force in the x-direction may be obtained using the Equation (1)

xref bw AC v F ,2

2

1⋅⋅⋅⋅= ρ (1)

where: ρ is the density of air,vb is the basic wind velocity,C is the wind load factor for bridges, Aref,x is the reference area.The values for ρ may be given by the NationalAnnex, while the recommended value is 1,25 kg/m3.The basic wind velocity is defined as:

0,b seasondir b vccv ⋅⋅= (2)

where:C dir is the directional factor (various winddirections may be found in the National Annex; therecommended value is 1,0),C season is the seasonal factor (may be given in the National Annex; the recommended value is 1,0),

Figure 1. Cross-sections of normal construction decks [8]

Figure 2. Directions of wind actions on bridges


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Eng. Rev. 31-1 (2011) 45-54 47 _______________________________________________________________________________________________________________________

vb,0 is the fundamental value of the basic windvelocity defined as the characteristic 10 minutesmean wind velocity at 10 m above ground of terraincategory II.

The wind load factor C is determined by the

following equation:

x f e c zcC ,)( ⋅= (3)

where:ce(z) is the exposure factor,c f,x is the force coefficients in the x-direction.Force coefficient for wind actions on bridge decksin the x–direction is given by:

0,, fx x f cc = (4)

where:c fx,0 is the force coefficient without free-end flow.For normal bridges c fx,0 may be taken equal to 1,3.Alternatively, c fx,0 may be taken from Figure 3.For a flat terrain, where the orography factorco(z)=1,0, the exposure factor ce(z) can bedetermined from Figure 4. It is a function of heightabove ground level and a function of terraincategory.The standard EN 1991-1-4 [8] defines five differentterrain categories:0 - sea or coastal area exposed to the open sea,I - lakes or flat and horizontal area with negligible

vegetation and without obstacles,II - area with low vegetation such as grass andisolated obstacles (trees, buildings) with separationsof at least 20 obstacle heights,III - area with regular cover of vegetation or buildings or with isolated obstacles with separationsof a maximum of 20 obstacle heights (such asvillages, suburban terrain, permanent forest), IV -area in which at least 15% of the surface is coveredwith buildings and their average height exceeds 15m.The reference area Aref,x for decks with plain beamsor webs without traffic should be defined as:

Ld A tot xref ⋅=, (5)

where 1d d d tot += is defined according to Figure 5

and Table 1; L is length of a span of the bridge deck.

3. PARAMETRIC ANALYSIS

In the paper, the effect of wind on the slab beam bridge deck shown in Figure 6 is analyzed. Thistype of bridge deck is very usual, so similar deck

structures can be found at various locations inCroatia, in different environments, and at differentheights above ground level. Also, different types ofroad restraint system can be built on it. All these parameters affect the wind load on the deck.Therefore, in this paper, parametric analysis of windload on a slab beam bridge deck as shown in Figure6 will be conducted varying the road restraintsystem (open parapet for pedestrians, a solidconcrete safety barrier height of 1.1 m and an open parapet for pedestrians together with an open safety barrier), the height of deck above ground level (5,10, 15 and 20 m), the terrain category (0 to IV) and

differing wind area (I toV).

3.1. Defining the parameters for the calculation

To calculate the wind load on the bridge deck inaccordance with Equation (1), it is necessary todetermine the following parameters: the density ofair ρ, the basic wind velocity vb, the wind load factorC and the reference area Aref,x.

3.1.1. The density of air

Recommended value 25,1= ρ kg/m3 is taken into

account [13].

3.1.2. The basic wind velocity

The basic wind velocity is determined according toEquation (2). The directional factor cdir =1 and theseason factor c season =1 [13].The fundamental value of the basic wind velocityvb,0 is defined in the National Annex [13]. Accordingto [13], Croatia is divided into five wind areas, asshown in Figure 7.

3.1.3. The wind load factor

The force coefficient is defined by Equations (3)and (4) in Chapter 2.2.1.The force coefficient c f,x is shown in Table 2, independence of the road restraint system, depth andwidth of the deck. The exposure factor ce(z) isshown in Table 3, in dependence on the deck heightabove ground and the terrain category.


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Values d , d 1, d tot and b are determined according to

Figure 6 and Table 1. Terrain categories A, B and Care defined in Table 1. The values of c fx aredetermined from Figure 3 and ce(z) from Figure 4.

(a)

(b)

a) construction phase or open parapets (more than 50% open)

b) with parapets or noise barrier or traffic

Figure 3. Force coefficient c f,x for bridges [8]

Figure 4. Illustrations of the exposure factor ce(z) for co(z)=1,0 [8]

Opensafety barrier

OpenparapetSolidparapet or solid

safety barrier

d

d 1

Figure 5. Depth to be used for Aref,x [8]


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Eng. Rev. 31-1 (2011) 45-54 49 _______________________________________________________________________________________________________________________

Table 1. Depth d tot to be used for Aref,x

Road restraint system on one side on both sides

Open parapet or open safety barrier A d+0,3 m d+0,6 m

Open parapet and open safety barrier B d+0,6 m d+1,2 m

Solid parapet or solid safety barrier C d+d 1 d+2 d 1

3.1.4. The reference area

The reference area is defined by Equation (5), where L is 14,5 m and the values of d tot are shown in Table2.

3.2. Results

The results of the obtained parametric analysis areshown in Tables 4 to 8. The wind force F w acting onthe bridge deck in the x-direction is calculated byusing Equation (1) and varying the following parameters: height of the bridge deck above ground,the terrain category, the road restraint system andthe wind area.Some typical results are graphically shown in

Figures 8 to 10.

Figure 6. Analyzed bridge deck cross section

Wind area vb0

Figure 7. A graphic representation of wind areas in Croatia and the corresponding fundamental value of thebasic wind velocity


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Table 2. The force coefficient c f,x in dependence on road restraint system and deck dimensions

Road restraint systemd

[m]d 1

[m] d tot[m]

b[m]

b/d tot c f,x

A

1,03

0,6 1,63

10,1

6,20 1,3B 1,2 2,23 4,53 1,15

C 2,2 3,23 3,13 1,6

Table 3. The exposure coefficient ce(z) in dependence on height above ground and terrain category

ce(z)Terrain category

0 I II III IV

H e i g h t

a b o v e

g r o u n d

5 m 2,6 2,32 1,9 1,3 1,1910 m 3,0 2,75 2,35 1,7 1,1915 m 3,2 3,0 2,6 2,0 1,4520 m 3,4 3,2 2,8 2,2 1,65

Table 4. The wind force for I wind area

F w [kN]Height above ground

5 m 10 m 15 m 20 m

T e r r a i n c a t e g o r y

0

R o a d r e s t r a i n t s y s t e m

A 24,22 27,84 29,73 31,61B 29,29 33,79 35,96 38,28C 58,87 68,01 72,50 77,14

IA 21,61 25,52 27,84 29,73B 26,10 30,89 33,79 35,96C 52,64 62,35 68,01 72,50

IIA 17,69 21,90 24,22 25,96B 21,32 26,39 29,29 31,47C 43,07 53,22 58,87 63,51

IIIA 12,04 15,81 18,56 20,45B 14,65 19,14 22,48 24,80C 29,44 38,57 45,39 49,88

IV

A 11,02 11,02 13,49 15,37

B 13,34 13,34 16,24 18,56C 26,97 26,97 32,92 37,41

Table 5. The wind force for II wind area


5 m 10 m 15 m 20 m

T e r r a i n

c a t e g o r y

0


A 44,95 51,91 55,25 58,73B 54,38 62,79 66,99 71,05C 109,62 126,44 134,85 143,26

IA 40,17 47,56 51,91 55,25B 48,58 57,57 62,79 66,99C 97,73 115,86 126,44 134,85

II

A 32,77 40,60 44,95 48,43

B 39,73 49,16 54,38 58,58C 80,04 99,04 109,62 118,03

IIIA 22,48 29,44 34,51 37,99B 27,26 35,53 41,91 45,97C 54,81 71,63 84,25 92,80

IVA 20,59 20,59 25,09 28,57B 24,94 24,94 30,31 34,51C 50,17 50,17 61,19 69,60


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Eng. Rev. 31-1 (2011) 45-54 51 _______________________________________________________________________________________________________________________

Table 6. The wind force for III wind area


5 m 10 m 15 m 20 m


0


A 61,19 70,62 75,26 80,04B 73,95 85,41 91,06 96,86C 149,21 172,12 183,57 195,03

IA 54,52 64,67 70,62 75,26B 66,12 78,30 85,41 91,06C 133,11 157,76 172,12 183,57

IIA 44,66 55,25 61,19 65,83B 54,09 66,85 73,95 79,75C 109,04 134,85 149,21 160,66

IIIA 30,60 40,02 46,98 51,77B 36,98 48,43 56,99 62,64C 74,53 97,59 114,70 126,15

IVA 27,99 27,99 34,08 38,86B 33,93 33,93 41,33 46,98C 68,30 68,30 83,23 94,69

Table 7. The wind force for IV wind area


5 m 10 m 15 m 20 m


0


A 79,90 92,22 98,31 104,40B 96,72 111,51 119,05 126,44C 194,88 224,75 239,83 254,77

IA 71,34 84,54 92,22 98,31B 86,28 102,23 111,51 119,05C 173,86 206,05 224,75 239,83

IIA 58,44 72,21 79,90 85,99B 70,62 87,44 96,72 104,11C 142,39 176,03 194,88 209,82

IIIA 39,88 52,20 61,48 67,57B 48,29 63,22 74,39 81,78

C 97,44 127,46 149,93 164,87

IVA 36,54 36,54 44,52 50,75B 44,23 44,23 53,94 61,34C 89,18 89,18 108,61 123,69

Table 8. The wind force for V wind area


5 m 10 m 15 m 20 m


0

R o a d r e s t r a i n t

s y s t e m

A 124,85 143,99 153,70 163,27B 151,09 174,29 185,89 197,49C 304,50 351,34 374,68 398,17

IA 111,36 132,10 143,99 153,70B 134,85 159,79 174,29 185,89C 271,59 322,05 351,34 374,68

IIA 91,21 112,81 124,85 134,42B 110,35 136,59 151,09 162,69C 222,43 275,21 304,50 327,85

IIIA 62,35 81,64 95,99 105,56B 75,55 98,75 116,15 127,89C 152,25 199,09 234,18 257,67

IVA 57,13 57,13 69,60 79,17B 69,17 69,17 84,25 95,85C 139,35 139,35 169,80 193,14


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20 m15 m

10 m5 m

72,5068,01

62,35

52,64

35,96

33,7930,89

26,1029,73

27,8425,52 21,61

0

10

20

30

40

50

60

70

80

HEIGHT ABOVE GROUND

Solidparapet

ROAD RESTRAINT SYSTEM

W I N

D F O R C E

[kN]

Openparapet and open safety barrier

Openparapet

Figure 8. The wind force in I wind area and terrain category I, in dependance on height above ground androad restraint system

V IV III II I

304,50

194,88

149,21

109,62

58,87

271,59

173,86

133,11

97,73

52,64

222,43

142,39

109,04

80,04

43,07

152,25

97,44

74,53

54,81

29,44

139,35

89,18

68,30

50,17

26,970

50

100

150

200

250

300

350

WIND AREAS

TERRAIN CATEGORY

W I N D F O R C E

0

I

II

III

IV

[kN]

Figure 9. The wind force on 5 m of height above ground and with solid parapet, in dependance on wind areaand terrain category

0 I II III IV

58,73

55,25

48,43

37,99

28,58

55,25

51,91

44,95

34,51

25,09

51,91

47,56

40,6

29,44

20,59

44,95

40,17

32,77

22,48 20,59

0

10

20

30

40

50

60HEIGHT ABOVE GROUND

20 m

15 m

10 m

5 m

TERRAIN CATEGORY

W I N D F O R C E

[kN]

Figure 10. The wind force in II wind area and with open parapet, in dependance on terrain category andheight above ground


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Eng. Rev. 31-1 (2011) 45-54 53 _______________________________________________________________________________________________________________________

4. CONCLUSION

From the analysis of the results obtained in thisstudy we can conclude the following:1. The wind force acting on the deck of the analyzed

bridge, which is built in the same terrain category onthe same height above ground, with the same roadrestraint system, but in a different wind area,increases with increasing wind area (in the I windarea the force is the smallest and in the V wind areathe force is the greatest). The wind force increasesdue to an increase in the basic wind velocity. Theratio of wind forces for a certain wind area is asquare function of the ratio of their basic windvelocities.2. The wind force acting on the deck of the analyzed bridge, which is built in the same wind area, on thesame height above ground, with the same road

restraint system, but on the different terraincategory, decreases with increasing a terraincategory (on the terrain category 0 (coastal areaexposed to the open sea) the force is the greatest andon the terrain category IV (in cities) it is thesmallest). The maximum value of wind force can betwice as high as the minimum value for the same bridge.3. With the wind force acting on the deck of theanalyzed bridge, which is built in the same windarea and on the same terrain category, the same roadrestraint system increases due to an increase in theheight of the deck above ground. The wind force on

the deck at 20 m above ground is 30-40% greaterthan on the deck at 5 m above ground.4. The wind force acting on the deck of the analyzed bridge, which is built in same wind area on the same bridge deck height above ground on the same terraincategory, is different for different road restrainsystems. The smallest force acts on the bridge withan open pedestrian parapet. The force increases by20% if there is an open safety barrier besides anopen pedestrian parapet, and the greatest force is onthe bridge with a solid concrete parapet. Thegreatest force is 2.4 times greater than the minimalforce; the choice of open fences instead of a

concrete solid parapet on the same bridge canreduce the wind force by more than double.If we look closer at the results of parametricanalysis, it can be seen that the smallest wind force( F w = 11,02 kN) is calculated for a bridge built inthe I wind area, on the terrain category IV with a bridge deck at 5 or 10 m above ground and with anopen parapet (for instance a bridge built in the city

of Osijek). The greatest wind force ( F w= 398,17 kN)is calculated for a bridge built in the V wind area, onthe terrain category I, with a bridge deck at 20 mabove ground and with a solid parapet (for instancea bridge built in the coastal area of the Makarskaregion). As it can be seen from the analysis, windaction on a bridge deck may change drastically dueto the wind area, terrain category, road restraintsystem and bridge deck height above ground. Thesefacts must be taken into account when standardized bridges are built in different locations.

5. LIST OF SYMBOLS

wind force F w, kNdensity of air ρ, kg/ m3

basic wind velocity vb, m/swind load factor C , -

reference area Aref,x, m2

directional factor cdir , -

season factor c season,-fundamental value of the basicwind velocity vb,0, m/sexposure factor ce(z), -orography factor co(z), -force coefficients c f,x, -force coefficient withoutfree-end flow c fx,0, -calculating depth d tot , mlength of a span L, mwidth of a span deck b, m

REFERENCES

[1] Čaušević, M., Špalj, I., Žic, E.: Djelovanjevjetra na mostove prema europskoj normi,Građevinar, Vol. 60 (2008) No. 1, p. 21-35.

[2] Tehnič ki propis za betonske konstrukcije; Narodne novine br. 139/09, 14/10 i 125/10

[3] Tehnič ki propis za zidane konstrukcije; Narodne novine br. 1/07

[4] Tehnič ki propis za drvene konstrukcije; Narodne novine br. 121/07, 48/2009 i 125/10

[5] Tehnič ki propis za č elič ne konstrukcije; Narodne novine br. 112/08 i 1125/10[6] Tehnič ki propis za spregnute konstrukcije od

č elika i betona; Narodne novine br. 119/09 i125/10

[7] Council Directive 89/106/EEC on 21 December1988 on the approximation of laws, regulationsand administrative provisions of the Member


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States relating to construction products,Official Journal L 040, 11/02/1989

[8] EN 1991-1-4, Eurocode 1 – Actions on structures: Part 1-4: General actions – Windactions, CEN, Brusseles, 2005.

[9] Peroš, B., Boko, I., Šimunović, T., Kuzmanić,D.: Podloge za nove hrvatske norme zaopterećenje vjetrom, Građevinar, Vol. 60(2008) No. 4, p. 309-316.

[10] Bajić, A.: Oč ekivani režim strujanja vjetra naautocesti Sv. Rok (jug) – Maslenica,Građevinar, Vol. 55 (2003) No. 3, p. 149-158.

[11] Bajić, A., Peroš, B., Vučetić, V., Z Žibrat, Z.:Opterećenje vjetrom – meteorološka podloga za hrvatske norme, Građevinar, Vol. 53 (2001) No. 8, p. 495-505.

[12] Bajić, A., Peroš, B.: Referentna brzina vjetra –utjecaj perioda osrednjavanja, Građevinar,Vol. 53 (2001) No. 9, p. 555-562.

[13] HRN ENV 1991-2-4, Eurokod1: Osnove projektiranja i djelovanja na konstrukcije - 2-4.dio: Djelovanja na konstrukcije - Opterećenjevjetrom, Hrvatski zavod za norme, Zagreb,2005.

[14] Liker, B.: Opterećenje vjetrom rasponskog sklopa cestovnog mosta u ovisnosti o kategoriji zemljišta prema EN 1991-1-4, Završni rad,Rijeka, 2009.

Received: 10.02.2011.

Preliminary note

Authors’ addressdoc.dr.sc. Ivana Štimac Grandić, dipl.ing.građ.Ana Ivančić, univ. bacc. ing. aedif.Bojan Liker, univ. bacc. ing. aedif.Građevinski fakultet Sveučilišta u RijeciViktora Cara Emina 551000 [email protected]@gradri.hr [email protected]

Accepted: 16.05.2011.

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Parametric analysis of wind action on slab